CA-Based Interpretable Knowledge Representation and Analysis of Geometric Design Parameters

2026-03-18

AI Summary

This study addresses the challenge posed by high-dimensional CAD geometric design parameters, which complicate downstream simulation and optimization tasks. While conventional principal component analysis (PCA) struggles to accurately reconstruct the original interpretable parameters from reduced representations, this work systematically examines the impact of each PCA stage on geometric fidelity. It reveals the equivalence between domain-specific PCA variants and standard PCA, and establishes theoretical bounds and conditions under which interpretable parameter reconstruction is feasible. Through geometric parametrization modeling, interpretability analysis, and numerical experiments, the study demonstrates that, under specific conditions, original design parameters can be recovered from PCA representations with high accuracy. These findings provide both theoretical grounding and practical guidance for interpretable dimensionality reduction in high-dimensional geometric design spaces.

Technology Category

• Machine Learning: Dimensionality Reduction/Feature Selection
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Computer Vision: Interpretability, Explainability, and Transparency

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

In many CAD-based applications, complex geometries are defined by a high number of design parameters. This leads to high-dimensional design spaces that are challenging for downstream engineering processes like simulations, optimization, and design exploration tasks. Therefore, dimension reduction methods such as principal component analysis (PCA) are used. The PCA identifies dominant modes of geometric variation and yields a compact representation of the geometry. While classical PCA excels in the compact representation part, it does not directly recover underlying design parameters of a generated geometry. In this work, we deal with the problem of estimating design parameters from PCA-based representations. Analyzing a recent modification of the PCA dedicated to our field of application, we show that the results are actually identical to the standard PCA. We investigate limitations of this approach and present reasonable conditions under which accurate, interpretable parameter estimation can be obtained. With the help of dedicated experiments, we take a more in-depth look at every stage of the PCA and the possible changes of the geometry during these processes.

Problem

• design parameter estimation
• principal component analysis
• geometric representation
• dimensionality reduction
• CAD-based design

Innovation

• PCA
• design parameter estimation
• interpretable representation
• geometric variation
• dimensionality reduction